Finite Group Databasebeta

← #19143996

Subgroups — #19143996

Order 5504.

772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583735C211yesmaximal, characteristic, complemented
2#14583466C212yesmaximal, complemented
3#14583085C218yesmaximal, complemented
4#14582873C211yesmaximal, characteristic, complemented
5#14582872C212yesmaximal, complemented
6C43×#535C211yesmaximal, characteristic, complemented
7#13063373—21no—
8#13063372—22no—
9#13063371—22no—
10#13063370—21no—
11#13063370C2214yes—
12C2×#10621898—22no—
13C2×#10621898C2212yes—
14#41×D43—24no—
15#13063321—22no—
16#13063312—22no—
17#13063296—24no—
18#13063294C2218yescomplemented
19#13063284C2212yescomplemented
20#13063240C2214yescomplemented
21#13063239C2218yescomplemented
22C2×#41×C43C2211yescharacteristic
23C22×D4×C43C2211yescharacteristic, complemented
24#127×C43—21no—
25#124×C43—21no—
26#121×C43—22no—
27#120×C43C2214yescomplemented
28#117×C43C2211yescharacteristic, complemented
29C24×C43C2312yes—
30#41×C43—22no—
31#41×C43—22no—
32C2×Q8×C43D411yescharacteristic, complemented
33C2×D4×C43—21no—
34C2×D4×C43—21no—
35C2×D4×C43—22no—
36C2×D4×C43—22no—
37C2×D4×C43—24no—
38C2×D4×C43D411yescharacteristic, complemented
39C2×D4×C43C2312yes—
40C22×C4×C43D412yescomplemented
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—24no—
43C2×C22⋊D43—28no—
44C2×C22⋊D43C2314yes—
45#10621902—24no—
46Q8×D43—24no—
47#10621900—24no—
48#10621900—28no—
49D4×D43—24no—
50D4×D43—28no—
51#10621898—24no—
52#10621898—24no—
53#10621898—22no—
54#10621898—22no—
55#10621898—24no—
56#10621898—22no—
57#10621898—22no—
58C2×D172—22no—
59C2×D172D412yescomplemented
60C2×C4×D43—24no—
61C2×C4×D43D414yescomplemented
62C2×Dic86—22no—
63C2×Dic86D412yescomplemented
64C4⋊C4×C43—21no—
65C22⋊C4×C43—24no—
66C22⋊C4×C43C2312yes—
67C42×C43—21no—
68C22⋊Dic43—28no—
69C22⋊Dic43C2314yes—
70C4⋊Dic43—22no—
71C4×Dic43—22no—
72C23×C43—24no—
73C23×C43—22no—
74C23×C43—82no—
75C23×C43C2×D412yes—
76C23×C43C2411yescharacteristic
77C22×D43—24no—
78C22×D43C2×D414yes—
79Q8×C43—22no—
80D4×C43—24no—
81D4×C43—22no—
82D4×C43—41no—
83D4×C43—42no—
84D4×C43—41no—
85D4×C43—84no—
86C2×C4×C43—22no—
87C2×C4×C43—22no—
88C2×C4×C43—22no—
89C2×C4×C43C2×D412yes—
90C2×C4×C43C2×D412yes—
91C2×C4×C43C2×D412yes—
92C2×C4×C43C2×D411yescharacteristic
93C2×C4×C43C2×D411yescharacteristic
94C22⋊D43—28no—
95C22⋊D43—24no—
96C22⋊D43—24no—
97C22⋊D43—88no—
98C2×Dic43—24no—
99C2×Dic43—24no—
100C2×Dic43C2×D414yes—
101D172—24no—
102D172—22no—
103D172—22no—
104C4×D43—28no—
105C4×D43—24no—
106C4×D43—24no—
107Dic86—24no—
108Dic86—22no—
109Dic86—22no—
110C22×C43—22no—
111C22×C43—41no—
112C22×C43—42no—
113C22×C43—48no—
114C22×C43—44no—
115C22×C43—42no—
116C22×C43C22×D412yes—
117C22×C43C22×D411yescharacteristic
118C2×D43—24no—
119C2×D43—44no—
120C2×D43—84no—
121C4×C43—22no—
122C4×C43—42no—
123C4×C43#12011yescharacteristic
124C4×C43#12012yes—
125C4×C43#12011yescharacteristic
126Dic43—24no—
127Dic43—44no—
128#3027—431nomaximal, Sylow
129C2×C43—22no—
130C2×C43—21no—
131C2×C43—42no—
132C2×C43—82no—
133C2×C43C2×#12011yescharacteristic
134D43—44no—
135#585—431no—
136#535—432no—
137#535D4311yescharacteristic, complemented
138B(4,𝔽2)—438no—
139#410—431no—
140#410—432no—
141C43#302711yescharacteristic, complemented, Sylow
1422−1+4—862no—
1432−1+4—861no—
144H(5,𝔽2)—434no—
145H(5,𝔽2)—862no—
146H(5,𝔽2)—861no—
147C2×#41—432no—
148C2×#41—864no—
149C2×#41—862no—
150C2×#41C2×D4311yescharacteristic
151C22×D4C2×D4311yescharacteristic, complemented
152#127—21no—
153#127—862no—
154#124—21no—
155#124—862no—
156#121—22no—
157#121—864no—
158#120—438no—
159#120C2×D4314yescomplemented
160#117—432no—
161#117C2×D4311yescharacteristic, complemented
162#99—434no—
163#99—438no—
164C24C22×D4312yes—
165#41—22no—
166#41—22no—
167#41—864no—
168#41—864no—
169#41—868no—
170#41—864no—
171#41—864no—
172#41—862no—
173#41—862no—
174#41—862no—
175#41—862no—
176#41—864no—
177C2×Q8—432no—
178C2×Q8—862no—
179C2×Q8—864no—
180C2×Q8C22⋊D4311yescharacteristic, complemented
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—434no—
187C2×D4—432no—
188C2×D4—862no—
189C2×D4—868no—
190C2×D4—864no—
191C2×D4—864no—
192C2×D4—868no—
193C2×D4C22⋊D4311yescharacteristic, complemented
194C2×D4C22×D4312yes—
195C22×C4—434no—
196C22×C4—864no—
197C22×C4C22⋊D4312yescomplemented
198C22×C4C22×D4311yescharacteristic
199C4⋊C4—21no—
200C4⋊C4—862no—
201C22⋊C4—24no—
202C22⋊C4—434no—
203C22⋊C4—868no—
204C22⋊C4C22×D4312yes—
205C42—21no—
206C42—862no—
207C23—24no—
208C23—22no—
209C23—82no—
210C23—434no—
211C23—864no—
212C23C2×C22⋊D4312yes—
213C23C23×D4311yescharacteristic
214Q8—22no—
215Q8—864no—
216Q8—862no—
217Q8—862no—
218D4—24no—
219D4—22no—
220D4—41no—
221D4—41no—
222D4—42no—
223D4—84no—
224D4—864no—
225D4—868no—
226D4—864no—
227D4—864no—
228D4—862no—
229D4—862no—
230D4—3448no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—434no—
235C2×C4—868no—
236C2×C4—864no—
237C2×C4—864no—
238C2×C4—864no—
239C2×C4—864no—
240C2×C4D4×D4312yes—
241C2×C4D4×D4312yes—
242C2×C4C2×C22⋊D4312yes—
243C2×C4C2×C22⋊D4311yescharacteristic
244C2×C4C2×C22⋊D4311yescharacteristic
245C22—22no—
246C22—41no—
247C22—42no—
248C22—44no—
249C22—48no—
250C22—42no—
251C22—864no—
252C22—3444no—
253C22—1724no—
254C22C2×D4×D4312yes—
255C22C22×C22⋊D4311yescharacteristic
256C4—22no—
257C4—42no—
258C4—864no—
259C4—1724no—
260C4#1306329311yescharacteristic
261C4#1306329311yescharacteristic
262C4#1306329312yes—
263C2—21no—
264C2—22no—
265C2—42no—
266C2—82no—
267C2—1724no—
268C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC43×#535C2
socleC2×C43C2×#120
hypercenter#535D43
hypocenterC43#3027
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #535

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14583735C2semidirect
2. #14583466C2semidirect
3. #14583085C2semidirect
4. #14582873C2semidirect
5. #14582872C2semidirect
6. C43×#535C2semidirect
18. #13063294C22semidirect
19. #13063284C22semidirect
20. #13063240C22semidirect
21. #13063239C22semidirect
23. C22×D4×C43C22semidirect
27. #120×C43C22semidirect
28. #117×C43C22semidirect
32. C2×Q8×C43D4semidirect
38. C2×D4×C43D4semidirect
40. C22×C4×C43D4semidirect
59. C2×D172D4semidirect
61. C2×C4×D43D4semidirect
63. C2×Dic86D4semidirect
137. #535D43semidirect
141. C43#3027semidirect
151. C22×D4C2×D43semidirect
159. #120C2×D43semidirect
161. #117C2×D43semidirect
180. C2×Q8C22⋊D43semidirect
193. C2×D4C22⋊D43semidirect
197. C22×C4C22⋊D43semidirect